of gauge theories Nick Evans University of Southampton New - - PowerPoint PPT Presentation
Dynamic AdS/QCD and the spectra of gauge theories Nick Evans University of Southampton New understanding of holographic descriptions of mesons A stab at predicting the spectra of arbitrary AF gauge theories Oxford October 2014 Back
New understanding of holographic descriptions
A stab at predicting the spectra of arbitrary AF gauge theories
Bottom up AdS/QCD
Orthonormal wave functions
Dilaton Flow Geometry: Gubser, Sfetsos Here, this is just a simple, back reacted, repulsive, hard wall…. Babington et al, Ghoroku..
Erdmenger, NE,Kirsch, Threlfall 0711.4467
These models live at very large coupling – QCD is at intermediate coupling strength… The running coupling is rather different (UV strong fixed point) Success beyond caricature seems surprising… how does one improve towards QCD?
Top down models of chiral symmetry breaking
Parameter count r c = qq m g
Son, Stephanov, Erlich, Katz
IR improve – include all operators that are non-zero in the vacuum and back react them on each other UV perfect – need to match the running of operators to the true perturbative QCD values in the UV…. No dynamics – inputing condensate and hard wall and fitting is only dynamics…. Of course as in any effective description of QCD this is overwhelming and you end up just re-parameterizing the data…. In QCD the regime of validity of the gravity description is very tight… The basic ideas are remarkably good… but… to systematically move to QCD we would need to:
It had been quite hard to understand how to put in the dynamics of an individual gauge theory…
Holographic Models for QCD in the Veneziano Limit Matti Jarvinen, Elias Kiritsis 1112.1261 We model the qq condensate by a scalar in “AdS”… Breitenlohner-Freedman Bound A scalar in AdS is stable until msq < - 4 ie D < 2 A hard prediction that matches gap equation-ology for the on-set of chiral symmetry breaking… Holographic models work for QCD mesons because they are describing the running of the anomalous dimension of qq rather than the running of the coupling…
Alvares, NE, Kim, 1204.2474
l m Nf/Nc = 3.. 4.5 For example if we try to (very naively) input the two loop QCD running of the coupling… We output these running masses… to be compared with the perturbative expectation below…
Top-down probe-brane models of QCD are just AdS/QCD with the background providing a running g…
D7 probe action in AdS expanded to quadratic order X is now a dynamical field whose solution will determine the condensate as a function of m We use the top-down IR boundary condition on mass-shell: X’(r=X) = 0 X enters into the AdS metric to cut off the radial scale at the value of m or the condensate – no hard wall The gauge DYNAMICS is input through Dm
The only free parameters are Nc, Nf, m, L
Timo Alho, NE, KimmoTuominen 1307.4896
L r Shoot out with L’(r=L) = 0 Read off m and qq in the UV… Nc=3, Nf=9 Now solve for meson masses by looking at linearized fluctuations about this vacuum…
M_rho = 1 defines L Real QCD lies here
There is very little Nc dependence Comparison to quenched lattice data (Bali et al… arXiv1304.4437) All of these models lie within 10% on any point....
Lattice data high due to extrapolation?
M_rho = M_pi
M_rho = 1 defines L Real QCD lies here M_rho = M_pi
We do see new behaviour as Nf heads towards 12….
No AF CFT c SB
Nf=11/2 Nc Nf = 4 Nc
Yamawaki,Appelquist, Terning, Sannino,… l m
Nf/Nc = 3.. 4.5
We indeed see a light sigma relative to the rho…
The QCD point is not right for the f0(500) but about right for the f0(980) – is the f0(500)
molecule ???
Alho, NE, Tuominen 1307.4896
Input (assumed) running of g for any theory you fancy…
The model concentrates on the quark states… we’re not trying to describe the running of the coupling or Tr F^2… however for us roughly… Find the dynamical IR quark mass… below that scale run the coupling as pure YM.. Find the IR pole… multiply by 8 and that’s the glueball mass! SU(3) Nf=3
SU(3) Nf=3 SU(3) Nf=11
For Nf > 4 Nc there is no dynamical scale so study the theory at non-zero quark mass… b=1 for the conformal IR and UV regimes but deviates at the intermediate running scale…
Holographic models of QCD continue to improve… running of g is crucial…one gets a good description of the lowest lying spectra at better than 10% and you can see generic behaviours with Nc Nf easily... Holography is a remarkably simple method to get a ball park answer for behaviour… but it still can’t be systematically improved… Hopefully Models are useful to guide lattice practitioners… On going work: T m phase structure… pomeron physics… enlarging to the full QCD spectra… why can I ignore other operators?